• Adjusted profile likelihood;
  • Bartlett adjustment;
  • Likelihood ratio test;
  • Residual maximum likelihood;
  • Restricted maximum likelihood

Likelihood ratio tests for fixed model terms are proposed for the analysis of linear mixed models when using residual maximum likelihood estimation. Bartlett-type adjustments, using an approximate decomposition of the data, are developed for the test statistics. A simulation study is used to compare properties of the test statistics proposed, with or without adjustment, with a Wald test. A proposed test statistic constructed by dropping fixed terms from the full fixed model is shown to give a better approximation to the asymptotic χ2-distribution than the Wald test for small data sets. Bartlett adjustment is shown to improve the χ2-approximation for the proposed tests substantially.